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\section{Marginal Log-Likelihood}
Library:
\begin{equation}
	log p(X) = - \frac{1}{2}(f(X)-m)'(K(X,X)-I\sigma_n^2)^{-1} (f(X)-m) - \frac{1}{2} log|K(X,X)-I\sigma_n^2 | - \frac{1}{2}n log(2 \pi \sigma_n^2)
\end{equation}
Book:
\begin{equation}
	log p(X) = - \frac{1}{2}(y-m)'* (K-I\sigma_n^2)^{-1} * (y-m) - \frac{1}{2} log|K-I\sigma_n^2 | - \frac{1}{2} nlog(2 \pi)
\end{equation}

\section{Prediction}
\begin{align}
	f(X*) &= m(X^*) + K(\theta,X^*,X)' (K(X,X)-I\sigma_n^2)^{-1} (f(X)-m(X))\\
	\sigma(X*) &= K(\theta,X^*,X^*) - K(\theta,X^*,X)' (K(X,X)-I\sigma_n^2)^{-1} K(\theta,X^*,X)
\end{align}

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